Mass transfer and bioavailability of PAH compounds in coal tar NAPL-slurry systems .1. Model development

A modeling framework is developed that addresses mass transfer, bioavailability, and potential biotreatment rates that may be achieved under stable microbial conditions in slurry systems containing multi-component non-aqueous-phase liquids (NAPLs). The framework is applied to describe biotreatment of polynuclear aromatic hydrocarbons (PAHs) released from coal tar NAPL in solid-slurry and liquid-liquid dispersion systems. A multi-step mass transport-degradation model considers equilibrium partitioning of PAH compound at the NAPL-water interface, followed by three sequential kinetic processes occurring in the aqueous phase: micropore sorption-diffusion, bulk aqueous-phase transport, and first-order biodegradation of bulk-phase substrate. Dynamic changes in NAPL-water equilibria due to depletion of PAH compound from the NAPL are incorporated into the model. Model results indicate that the overall rate of biotransformation of organic compounds from NAPLs is controlled by NAPL-water equilibrium processes represented by a dimensionless solubility factor, as well as the slowest of three aqueous-phase kinetic processes determined by pair-wise analysis of the dimensionless Blot number, the Thiele modulus, and the Damkohler number. Analytical equations and computer simulations demonstrate the utility of the dimensionless parameters in quantifying bioavailability, identifying dominant rate-limiting processes, and developing simpler models for biotransformation in NAPL-slurry systems. Some aspects of the modeling framework are evaluated in a companion paper using data from controlled laboratory experiments.